def _(expr, assumptions):
"""
* Unbounded ** NonZero -> Unbounded
* Bounded ** Bounded -> Bounded
* Abs()<=1 ** Positive -> Bounded
* Abs()>=1 ** Negative -> Bounded
* Otherwise unknown
"""
if expr.base == E:
return ask(Q.finite(expr.exp), assumptions)
base_bounded = ask(Q.finite(expr.base), assumptions)
exp_bounded = ask(Q.finite(expr.exp), assumptions)
if base_bounded is None and exp_bounded is None: # Common Case
return None
if base_bounded is False and ask(Q.extended_nonzero(expr.exp), assumptions):
return False
if base_bounded and exp_bounded:
return True
if (abs(expr.base) <= 1) == True and ask(Q.extended_positive(expr.exp), assumptions):
return True
if (abs(expr.base) >= 1) == True and ask(Q.extended_negative(expr.exp), assumptions):
return True
if (abs(expr.base) >= 1) == True and exp_bounded is False:
return False
return None
def _(expr, assumptions):
"""
Return True if expr is bounded, False if not and None if unknown.
Truth Table:
+---+---+---+--------+
| | | | |
| | B | U | ? |
| | | | |
+---+---+---+---+----+
| | | | | |
| | | | s | /s |
| | | | | |
+---+---+---+---+----+
| | | | |
| B | B | U | ? |
| | | | |
+---+---+---+---+----+
| | | | | |
| U | | U | U | ? |
| | | | | |
+---+---+---+---+----+
| | | | |
| ? | | | ? |
| | | | |
+---+---+---+---+----+
* B = Bounded
* U = Unbounded
* ? = unknown boundedness
* s = signed (hence nonzero)
* /s = not signed
"""
result = True
for arg in expr.args:
_bounded = ask(Q.finite(arg), assumptions)
if _bounded:
continue
elif _bounded is None:
if result is None:
return None
if ask(Q.extended_nonzero(arg), assumptions) is None:
return None
if result is not False:
result = None
else:
result = False
return result
